The answer is 2005
the last time was 2004-2005, both auburn and Utah went undefeated. USC won the championship.
Boise state Alabama Auburn Utah
The Auburn Tigers were the last SEC team to go undefeated. They went 11-0 in the reg season on their way to defeating Tennessee in the SEC championship game, then Virginia Tech in the Sugar Bowl. Auburn was snubbed by the BCS and passed over to play in the National Title game in favor of USC and Oklahoma who both also had undefeated regular season.
The last men's team to go undefeated during the regular season and win the tournament was Indiana in 1976.
The Steelers never had an undefeated season. They started off 4-0 in 2010 and in 1979. They started the season 7-0 in 1978.
LSU with two losses in 2007
Collingwood have done it back in 1929 or something
UNLV was undefeated in the regular season during the 1991 season, eventually losing to Duke in the NCAA tournament. Indiana University was the last team to go undefeated during the regular and post season. They were 32-0 in 1976.
No NFL teams went undefeated in 2009.